Patterns, Functions and Algebra
What you must understand
Candidates should continue number patterns, describe the rule in words, and find missing terms. You need to recognise sequences that increase by a constant difference (for example 4, 7, 10, 13, adding 3) and simple doubling or halving patterns. Algebra at this level means using a letter for an unknown, forming simple equations, and solving them by balancing. You should also substitute numbers into simple formulas such as perimeter = 2(l + w) and use function machines in both directions.
Traps to watch
- Finding the rule from one step: check the difference between several pairs of terms, not just the first two.
- Position versus term: in the sequence 5, 8, 11, …, the 1st term is 5, not 8. The rule is often "multiply the position by the difference and adjust".
- Solving equations: whatever you do to one side, do to the other. To undo "+ 7", subtract 7.
- Substitution: replace the letter with the number and follow order of operations; 3n means 3 × n, not 3 + n.
- Reverse function machines: work backwards and swap each operation for its inverse.
Worked example
A pattern uses matchsticks: 1 square uses 4 sticks, 2 squares in a row use 7, 3 squares use 10. How many sticks for 10 squares?
The rule is 3 sticks per extra square plus 1: sticks = 3n + 1. For n = 10, sticks = 3 × 10 + 1 = 31.
Rule of thumb: for a linear pattern, find the constant difference first, then test whether "difference × position + a fixed number" gives the terms.